Answer: a. 20 and b.10
Step-by-step explanation:
Given Letters = A, B, C, D, and E
Number of letters given = 5
a. When we choose 2 letters, without replacement from the 5 letters and order of the choices is relevant we use permutations.
Then, the number of ways we can choose 2 letters from 5 = [tex]^5P_2[/tex]
[tex]=\dfrac{5!}{(5-2)!}=\dfrac{5\times4\times3!}{3!}=20[/tex] [∵ [tex]^nP_r=\dfrac{n!}{(n-r)!}[/tex]]
So , when order of the choices is relevant , the total number of way to do this = 20
b. When we choose 2 letters, without replacement from the 5 letters and order of the choices is not relevant we use combinations.
Then, the number of ways we can choose 2 letters from 5 = [tex]^5C_2[/tex]
[tex]=\dfrac{5!}{2!(5-2)!}=\dfrac{5\times4\times3!}{2\times3!}=10[/tex] [∵ [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]]
So , when order of the choices is not relevant , the total number of way to do this = 10
